When Utah BYU left the WAC and formed the MWC many media outlets still placed BYU and Utah in the WAC conference. It took sometime before several media outlets acknowledged the MWC.
The Pac12 and the U of U wanted to seperate Utah from their old conference and do a better job at marketing their new conference affiliation. Which is why you see more Utah Pac12 gear than for any school in the Pac12.
The Pac12 merchandise also had an economic impact on the University of Utah apperal division. Because Ute fans wanted to celebrate being invited to the Pac12.
I have spoken to a Utah official and he said all conference schools are required to market their Pac12 affiliation and if you go to each's schools bookstore you will find a section with Pac12 items. The school can carry as much or as little but they must carry some items and the U is scaling back on what they offer.
But you said you never see USC'S or UCLA'S here is a link to USC'S bookstore offerings of PAC12 items.
Shop.usctrojans.com/search/pac12
You can do the same search for every PAC12 school they all have items refering them as members of the PAC12